Practice Test 36 - AP Statistics

20 questions. Answer them in any order, then submit to see your score and every explanation.

A librarian summarized the number of books checked out per patron during one month for a random sample of 140 patrons. The summaries were: mean $=3.8$ books, median $=3$ books, SD $=2.9$ books, five-number summary $(0,\ 1,\ 3,\ 5,\ 16)$ , and IQR $=4$ books. Which interpretation is correct?
A biologist measures 20 plants of the same species, recording $x$ = hours of sunlight per day and $y$ = weekly growth (cm). The regression of growth on sunlight yields a 99% confidence interval for the population slope $\beta$ of $(-0.4,\ 1.6)$ . Which interpretation is correct?
Researchers surveyed commuters who either took the Bus or Drove a car and asked whether they were satisfied with their commute (Satisfied/Not satisfied). The purpose is to compare conditional proportions of satisfaction by commute type. Based on the two-way table, which comparison is supported? Two-way table of Commute Type by Satisfaction (proportions of all commuters): - Bus & Satisfied: 0.24, Bus & Not satisfied: 0.16 - Drive & Satisfied: 0.30, Drive & Not satisfied: 0.30
A retailer is comparing two email subject lines to see which leads to a higher proportion of customers making a purchase within 24 hours. Of 500 customers emailed subject line A, 62 made a purchase; of 480 customers emailed subject line B, 45 made a purchase. The research claim is that subject line A has a higher purchase proportion. Which hypotheses are appropriate?
A university takes one random sample of 300 undergraduates and records each student's housing type (On-campus, Off-campus, With family) and class year (First-year, Sophomore, Junior/Senior). The results are summarized below. Which chi-square test is appropriate, and what are the correct hypotheses? (This is one sample with two categorical variables.)
A university health center believes that the proportion of all students who have received a flu shot this season is different from $55\%$ . A simple random sample of $n=180$ students finds $90$ who have received a flu shot (so $\hat{p}=0.50$ ). Which hypotheses are appropriate?
An engineer studies the relationship between operating temperature ( $x$ , in $^\circ$ C) and battery life ( $y$ , in hours) for 25 batteries and fits a least-squares regression line. A 99% confidence interval for the true slope is $(-0.30,\ 0.05)$ hours per $^\circ$ C. Which interpretation is correct?
A school district uses a random sample of students to estimate whether a new tutoring program increases the proportion of students passing Algebra I. The district will expand the program to all schools if the sample evidence suggests a higher pass rate. If the inference is wrong, the district could spend limited funds on a program that doesn't help, or fail to expand a program that would benefit many students. Why is it important to consider potential error when making this decision from the sample?
A school nurse wants to study whether students who sleep more tend to report lower stress. For each of 60 randomly selected students (the observational units), the nurse records hours of sleep last night and stress level on a 1–5 scale where 1 = not stressed and 5 = very stressed. The research goal is to see whether sleep helps predict stress. Which classification is correct?
A sports scientist compares the proportion of athletes who report improved performance after using two training plans. From independent random samples, a 90% confidence interval for the difference in improvement proportions (Plan A minus Plan B) is $(-0.03, 0.09)$ . Which interpretation is correct?
A school administrator investigates whether class size is related to average end-of-year math score. For a random sample of 55 classes, the administrator records class size (explanatory variable $x$ ) and average math score (response variable $y$ ) and fits a regression line predicting score from class size. The claim is that larger classes are associated with lower scores, implying a negative population slope. Which hypotheses are appropriate for testing this claim about the slope of the population regression line?
A marketing team tests two website layouts. For one week, the site uses Layout 1; the next week, it uses Layout 2. The purchase rate is 3.1% during the Layout 1 week and 3.8% during the Layout 2 week. No other data are collected. Which conclusion is supported by these data?
An economist studied $n=18$ countries and recorded gross domestic product per capita ( $x$ , in thousands of dollars) and average life expectancy ( $y$ , in years). A least-squares regression of life expectancy on GDP per capita produced slope $b_1=0.62$ . To assess whether the population slope differs from 0, the economist tested $H_0: \beta_1=0$ versus $H_a: \beta_1\ne 0$ and obtained a p-value of $0.083$ . At the $\alpha=0.05$ level, what conclusion is appropriate?
An ecologist models the relationship between average daily temperature ( $^{\circ}$ C) and the number of butterflies observed in a field. The ecologist claims that higher temperatures are associated with fewer butterflies. A 90% confidence interval for the slope is $(-1.5, -0.2)$ butterflies per $^{\circ}$ C. Is the claim supported by the confidence interval?
A local gym records the ages of its members. The data reveal a large number of members between 20 and 35 years old and another large number of members between 55 and 70 years old, with very few members in between these two ranges. Which unusual feature is present in this distribution?
A political scientist claims that, in a certain county, party affiliation among registered voters is 45% Party X, 35% Party Y, and 20% Independent. A random sample of 300 registered voters yields: Party X 120, Party Y 118, Independent 62. A chi-square goodness-of-fit test is conducted and reports $p$ -value = 0.014. Expected counts under $H_0$ are: Party X 135, Party Y 105, Independent 60. What conclusion is appropriate at the $\alpha=0.05$ level?
A cereal company advertises that the mean weight of cereal in its "18 oz" boxes is 18.0 ounces. A consumer group wants to test whether the true mean weight is less than 18.0 ounces. A random sample of $n=50$ boxes is weighed, and the sample mean is $\bar{x}=17.8$ ounces. Which hypotheses are appropriate for a test of the population mean box weight, $\mu$ ?
A real estate analyst fits a regression of home sale price ( $y$ , in thousands of dollars) on home size ( $x$ , in square feet). The analyst claims, "Each additional square foot increases the mean sale price." A 99% confidence interval for the slope is $( -0.002,\ 0.090)$ thousand dollars per square foot. Is the claim supported by the confidence interval?
An educator wants to know whether attendance category is related to whether a student passes a course. A random sample of students was selected, and each student was classified by attendance (High, Medium, Low) and course result (Pass, Fail). A chi-square test of independence was conducted at $\alpha=0.05$ . The observed counts and p-value are shown. What conclusion is appropriate?
A political scientist suspects that the proportion of voters who support a ballot measure differs between urban and rural counties. A random sample of 250 urban voters found 140 in favor ( $\hat{p}_U=0.56$ ), and an independent random sample of 220 rural voters found 99 in favor ( $\hat{p}_R=0.45$ ). The research claim is that support is different between the two populations. Which hypotheses are appropriate?

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